Sotheby’s and its largest investor, Daniel Loeb, will open their arguments in court on Tuesday on whether the auction house should be allowed to restrict the billionaire’s ownership stake, in a case that could reshape the world of shareholder activism.

Loeb, the head of hedge fund Third Point Capital Management who has been building a stake in Sotheby’s as he battles to win three seats on the company’s board, last month sued the 270-year-old auction house to remove its “poison pill” cap, arguing that it discriminates against activists.

Delaware Chancery Court Vice Chancellor Donald Parsons will hear arguments from both sides on whether Sotheby’s shareholder rights plan, which allows passive investors to buy as much as 20 percent in the company but caps active investors at 10 percent, is legal. A ruling is expected later in the week, ahead of Sotheby’s annual meeting scheduled for May 6.

The case could have wide implications for activist investing and corporate governance because it marks the first time that a judge will rule after an activist investor who has faced a poison pill has aired his grievances in court.

“The reason this is so important is that the idea that a pill can be used to stop an activist investor has never been approved,” said Robert Jackson, a law professor at Columbia University. “Whichever way the court rules will have lasting implications for the corporate landscape.”

Poison pills were originally designed to help companies defend against corporate raiders — the term given to investors seeking to take over a company with aggressive stock purchases — by limiting the amount of stock that can be bought.

But they have increasingly been used against activist shareholders, who seek changes to the way companies are managed, instead of vying for full control.

Air Products used a poison pill to keep William Ackman’s Pershing Square Capital Management from buying more than 10 percent in 2013, and Riverbed Technology used one against Elliott Management the same year.

The use of poison pills against activists seems to be picking up just as activists are becoming more popular in the hedge fund industry, attracting fresh money with strong returns.

This poison pill “is directed intentionally against shareholders exercising their rights,” said Marc Weingarten, a partner at law firm Schulte Roth & Zabel.

In the first three months of 2014, activist funds took in $3.5 billion in new assets, more than half of the $5.3 billion they took in for all of 2013, data from Hedge Fund Research show. Last year activist funds returned an average 16 percent, far more than the average hedge fund’s 9 percent gain.

Loeb’s $14.5 billion hedge fund Third Point gained 25.2 percent in 2013. That is the same year that he bought a 9.6 percent stake in Sotheby’s, as he compared it to “an old master painting in desperate need of restoration” and urged cost cuts, among other measures.

Lawyers who have been watching the case said there is no way to predict the outcome, in part because the courts have generally supported companies that use poison pills.

“In this case the company has good arguments on why it needs to have the pill in place and that restricting the ownership of passive investors could harm all investors,” said Keith Gottfried, a partner at law firm Alston & Bird who advises companies on shareholder activism. “Poison pills don’t prevent you from running a proxy contest.”